6958
2018
eng
420
435
2
271
article
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Robust Allocation of Operating Rooms: a Cutting Plane Approach to handle Lognormal Case Durations
The problem of allocating operating rooms (OR) to surgical cases is a challenging task, involving both combinatorial aspects
and uncertainty handling. We formulate this problem as a parallel machines scheduling problem, in which job durations follow a lognormal distribution,
and a fixed assignment of jobs to machines must be computed.
We propose a cutting-plane approach to solve the robust counterpart of this optimization problem.
To this end, we develop an algorithm based on fixed-point iterations that identifies worst-case scenarios and generates cut inequalities.
The main result of this article uses Hilbert's projective geometry to prove the convergence of this procedure under mild conditions.
We also propose two exact solution methods for a similar problem, but with a polyhedral uncertainty set, for which
only approximation approaches were known. Our model can
be extended to balance the load over several planning periods in a rolling horizon.
We present extensive numerical experiments for instances based on real data from a major hospital in Berlin. In particular, we find that:
(i) our approach performs well compared to a previous model that ignored the distribution of case durations;
(ii) compared to an alternative stochastic programming approach, robust optimization yields solutions that are more robust against uncertainty, at a small price in terms of average cost;
(iii) the \emph{longest expected processing time first} (LEPT) heuristic performs well and efficiently protects against extreme scenarios, but only if a good prediction model for the durations is available.
Finally, we draw a number of managerial implications from these observations.
European Journal of Operational Research
10.1016/j.ejor.2018.05.022
yes
urn:nbn:de:0297-zib-58502
Guillaume Sagnol
Guillaume Sagnol
Christoph Barner
Ralf Borndörfer
Mickaël Grima
Mathes Seeling
Claudia Spies
Klaus Wernecke
Mathematical Optimization
Borndörfer, Ralf
Sagnol, Guillaume
Charité-OPOSSUM
BMBF-IBOSS
Mathematics of Health Care